Strum
11th December 2007, 05:25 PM
Hi guys, I was just practicing for my upcoming Mechanics exam and was stuck on a couple practice questions... If anybody could help, it'd be much appreciated!
1. A particle P is projected vertically upwards from ground level at time t=0 with speed 20m/s. Two seconds later another particle Q is projected vertically upwards with speed 30m/s from a point on the same horizontal ground.
(a) Taking the upward direction as positive, write down expressions in terms of g and t for the velocities of P and Q t seconds after P is projected.
(b) Find the value of t when both particles are moving with the same speed.
3. Two trains S and T are moving with constant speeds on straight tracks which intersect at the point O. At 9:00am S has a position vector (-10i+24j) km and T has position vector 25j km relative to O, where i and j and unit vectors in directions due east and north respectively. S is movin with speed 52 km/h and T has speed 50 km/h, both towards O.
(a) Show that the velocity vector of S is (20i-48j) km/h and find the velocity vector of T.
(b) Find expressions for the position vectors of S and T at time t minutes after 9:00am.
(c) Show that the bearing of T from S remains constant during the motion and find this bearing.
1. A particle P is projected vertically upwards from ground level at time t=0 with speed 20m/s. Two seconds later another particle Q is projected vertically upwards with speed 30m/s from a point on the same horizontal ground.
(a) Taking the upward direction as positive, write down expressions in terms of g and t for the velocities of P and Q t seconds after P is projected.
(b) Find the value of t when both particles are moving with the same speed.
3. Two trains S and T are moving with constant speeds on straight tracks which intersect at the point O. At 9:00am S has a position vector (-10i+24j) km and T has position vector 25j km relative to O, where i and j and unit vectors in directions due east and north respectively. S is movin with speed 52 km/h and T has speed 50 km/h, both towards O.
(a) Show that the velocity vector of S is (20i-48j) km/h and find the velocity vector of T.
(b) Find expressions for the position vectors of S and T at time t minutes after 9:00am.
(c) Show that the bearing of T from S remains constant during the motion and find this bearing.